Finite Group Databasebeta

C2×C4×#88184 #16021345

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×C4×#88184

Splittings

FittingC23×C42×C13 ⋊ C2
SylowC13 ⋊ C2×C4×#121

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC23×C42×C13C2
socleC24×C13C24
prime radicalC22×#88184C2
cosocleC23×C13C25
hypercenterC23×C42D13
hypocenterC13C2×C4×#121
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C23×C42

5022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 327994);